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   -> Volume 6, Issue 10


Preprint: Wavelet Based Method for Nonlinear System Modeling
 
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Wayne Lawton (wlawton@iss.nus.sg)
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PostPosted: Thu Sep 18, 1997 11:00 pm    
Subject: Preprint: Wavelet Based Method for Nonlinear System Modeling
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#5 Preprint: Wavelet Based Method for Nonlinear System Modeling

Authors:

Wayne Lawton
Department of Mathematics
National University of Singapore
10 Kent Ridge Crescent, Singapore 119260

Yi Yu
Centre for Information Enhanced Medicine
National University of Singapore
Kent Ridge, Singapore 119597

Seng Luan Lee
Department of Mathematics
National University of Singapore
10 Kent Ridge Crescent, Singapore 119260

Shaohua Tan
Department of Electrical Engineering
National University of Singapore
10 Kent Ridge Crescent, Singapore 119260

Abstract:

This paper formulates the nonlinear system modeling problem as a
scattered data interpolation problem, and develops a new method that
computes interpolants that minimize a wavelet-based norm subject to
interpolatory constraints. The norm is that of a Reproducing Kernel
Hilbert Space (RKHS) for which the wavelet functions that form an
orthonormal basis for L^2 are orthogonal. In contrast to radial basis
function kernels, these kernels are not translation invariant and they
may be designed to provide spatially varying resolution useful for
interpolating from unevenly distributed data samples. Furthermore, the
discrete wavelet transform can be exploited to efficiently compute the
values of the interpolant on a uniform grid. Numerical simulations are
used to demonstrate the method.
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